Geodesic
Hamiltonians associated with the sixth Painlevé equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 54-65 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain the formula determining the general form of polynomial Hamiltonians associated with the sixth Painlevé equation and prove its uniqueness. We prove the existence of nonpolynomial Hamiltonians associated with this equation. We identify the Hamiltonian class for which the defining differential equation coincides with the equation ($h$-equation) for the simplest polynomial Hamiltonian (the Okamoto Hamiltonian).
Mots-clés : Painlevé equation, Heun equation.
Keywords: Hamiltonian, family of solutions, Bäcklund transformation 
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V. V. Tsegel'nik. Hamiltonians associated with the sixth Painlevé equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 54-65. http://geodesic.mathdoc.fr/item/TMF_2007_151_1_a3/

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